Control Applications

Scalable Nonlinear Programming Via Exact Differentiable Penalty Functions and Trust-Region Newton Methods

  • Mihai Anitescu
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization Tags , , , , ,

    We present an approach for nonlinear programming (NLP) based on the direct minimization of an exact di erentiable penalty function using trust-region Newton techniques. As opposed to existing algorithmic approaches to NLP, the approach provides all the features required for scalability: it can eciently detect and exploit directions of negative curvature, it is superlinearly convergent, and … Read more

    Convex computation of the region of attraction of polynomial control systems

  • Didier Henrion
  • Milan Korda
    • Categories Control Applications, Convex Optimization, Semi-definite Programming Tags , , , , , ,

    We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We show that the ROA can be computed by solving a convex linear programming (LP) problem over the … Read more

    Optimal management and sizing of energy storage under dynamic pricing for the efficient integration of renewable energy

  • Munther Dahleh
  • Pavithra Harsha
    • Categories Applications - OR and Management Sciences, Control Applications Tags , , , , , , , , ,

    In this paper, we address the optimal energy storage management and sizing problem in the presence of renewable energy and dynamic pricing. We formulate the problem as a stochastic dynamic programming problem that aims to minimize the long-term average cost of conventional generation used as well as investment in storage, if any, while satisfying all … Read more

    Optimal synthesis in the Reeds and Shepp problem with a onesided variation of velocity

  • Andrei V. Dmitruk
  • Ivan Samylovskiy
    • Categories Control Applications, Mechanical Engineering Tags , , , ,

    We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a onesided variation of the speed and a free final direction of velocity. Using Pontryagin Maximum Principle, we obtain all possible types of extremals and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis. Citation … Read more

    Linear System Identification via Atomic Norm Regularization

  • Badri Narayan Bhaskar
  • Benjamin Recht
  • Parikshit Shah
  • Gongguo Tang
    • Categories Control Applications, Convex Optimization Tags , , ,

    This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem that approximately solves the atomic norm minimization problem and identifies the unknown system from noisy linear measurements. … Read more

    Approximate Maximum Principle for Discrete Approximations of Optimal Control Systems with Nonsmooth Objectives and Endpoint Constraints

  • Boris S. Mordukhovich
  • Ilya Shvartsman
    • Categories Control Applications, Convex and Nonsmooth Optimization Tags , , ,

    The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finite-difference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate position between continuous-time and discrete-time (with fixed steps) control processes and play a significant role in both qualitative and numerical aspects of … Read more

    Sensitivity analysis for the outages of nuclear power plants

  • Kengy Barty
  • Joseph Frédéric Bonnans
  • Laurent Pfeiffer
    • Categories Control Applications Tags , , ,

    Nuclear power plants must be regularly shut down in order to perform refueling and maintenance operations. The scheduling of the outages is the first problem to be solved in electricity production management. It is a hard combinatorial problem for which an exact solving is impossible. Our approach consists in modelling the problem by a two-level … Read more

    Bundle method for non-convex minimization with inexact subgradients and function values

  • Dominikus Noll
    • Categories Control Applications, Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We discuss a bundle method to minimize non-smooth and non-convex locally Lipschitz functions. We analyze situations where only inexact subgradients or function values are available. For suitable classes of non-smooth functions we prove convergence of our algorithm to approximate critical points. Citation To appear in: Computational and Analytical Mathematics. Springer Proceedings in Mathematics Article Download … Read more

    Constraint Reduction with Exact Penalization for Model-Predictive Rotorcraft Control

  • Aaron L. Greenfield
  • Meiyun Y. He
  • Vineet Sahasrabudhe
  • André L. Tits
    • Categories Applications - Science and Engineering, Control Applications, Quadratic Programming Tags , , , , , , , , ,

    Model Predictive Control (also known as Receding Horizon Control (RHC)) has been highly successful in process control applications. Its use for aerospace applications has been hindered by its high computational requirements. In the present paper, we propose using enhanced primal-dual interior-point optimization techniques in the convex-quadratic-program-based RHC control of a rotorcraft. Our enhancements include a … Read more

    Algebraic Relaxations and Hardness Results in Polynomial Optimization and Lyapunov Analysis

  • Amir Ali Ahmadi
    • Categories Control Applications, Convex Optimization, Semi-definite Programming Tags , , , , ,

    The contributions of the first half of this thesis are on the computational and algebraic aspects of convexity in polynomial optimization. We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves … Read more